few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Multiply and divide within 100.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Understand properties of multiplication and the relationship between multiplication and division.

Rewrite rational expressions.

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.

Work with equal groups of objects to gain foundations for multiplication.

Represent and solve equations and inequalities graphically.

Work with radicals and integer exponents.

Write and interpret numerical expressions.

Interpret the structure of expressions.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Represent and solve problems involving multiplication and division.

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Perform arithmetic operations on polynomials.

Understand solving equations as a process of reasoning and explain the reasoning.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Generate and analyze patterns.

Use the four operations with whole numbers to solve problems.

Gain familiarity with factors and multiples.

Understand the connections between proportional relationships, lines, and linear equations.

Understand and apply properties of operations and the relationship between addition and subtraction.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Add and subtract within 20.

Write expressions in equivalent forms to solve problems.

Use polynomial identities to solve problems.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

Understand the relationship between zeros and factors of polynomials.
problem_activity: Narrative
The purpose of this activity is for students to create their own relevant mathematical questions and use their understanding of addition and subtraction to answer questions about their own and their peers' survey data.
Launch
Combine pairs into groups of 4
Activity
“Switch graphs. Use the sentence stems or create your own questions about the other group’s graphs.”
1
–
2 minutes: independent work time
4 minutes: partner work time.
“Take turns to ask each other the questions you came up with and use your own graph to answer.”
“When possible, write down an equation to show your reasoning.”
5 minutes: group discussion.
Monitor for students who write equations to show the categories they combine or compare when answering their peers' questions.
Student Facing
Trade graphs. Create questions about the other group’s graph.
Sentence stems:
How many students picked ___________ and __________ all together?
How many more students picked _______ than _______?
Take turns asking and answering questions.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students rely on counting to find solutions rather than adding or subtracting, consider asking "What equation could you write to represent the categories in the question?"
Activity Synthesis
Invite previously selected students to share.
“Where do we see the equations in their graph? What does the equation mean?”
“What’s the difference between answering the questions from a bar graph and answering them from a picture graph?”


correct_option_index: 21

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